I think the reasons go back further than natural/right turning waltzes.
In the days of the English and French courts when physical contact between partners was limited to the hands, gentlemen would have their ladies on their right side, away from the sword. Much of the dancing involved promenading the ladies around the room presenting and displaying their finery to the assembled audience. Hence the ladies were on the outside of the room and the procession moved anti-clockwise.
When the scandalous, outrageous close hold of the waltz became more acceptable, the ladies were held in the gentlemen's right arm again avoiding the scabbard etc. This offset hold and the existing practice of anticlockwise travel made the right turn the natural choice.
As for oval race tracks, could this go back to ancient Roman chariot races, whip in the right hand, reins in the left resulting in a tendency to curve to the left?
For motor races there are certainly some clockwise tracks including Brands Hatch in England.